Tidy Tuesday is a weekly podcast and community activity organized by the R4DS Online Learning Community, with the goal of helping R learners learn in real-world contexts. One of the datasets shared by TidyTuesday comes from Spotify and consists of 32,833 songs.3 After filtering down to unique tracks, there are 28,356 songs remaining. The distribution of song duration for these songs is moderately right skewed, with mean 226.6 seconds and standard deviation of 61.1 seconds.

a) For a random sample of 30 tracks from the list of unique songs, what is the expected mean song duration?

b) For a random sample of 30 tracks from the list of unique songs, what is the standard deviation of the mean song duration?

c) How many tracks would you need to (randomly) sample for the standard deviation of the sample mean song duration to equal 7 seconds?

d) Suppose that you create a randomly generated playlist of 50 songs to listen to during an upcoming flight. Compute the probability that the playlist duration is longer than 3 hours.